Partition_Type_All {MultiStatM}

Partitions, type and number of partitions

Description

Generates all partitions of N numbers and classify them by type

Usage

Partition_Type_All(N)

Arguments

N

The (integer) number of elements to be partitioned

Value

Part.class The list of all possible partitions given as partition matrices

S_N_r A vector with the number of partitions of size r=1, r=2, etc. (Stirling numbers of second kind )

eL_r A list of partition types with respect to partitions of size r=1, r=2, etc.

S_r_j Vectors of number of partitions with given types grouped by partitions of size r=1, r=2, etc.

References

Gy. Terdik, Multivariate statistical methods - going beyond the linear, Springer 2021. Case 1.4, p.31 and Example 1.18, p.32.

See Also

Other Partitions: Partition_2Perm(), Partition_Indecomposable(), Partition_Pairs(), Permutation_Inverse()

Examples

# See Example 1.18, p. 32, reference below
PTA<-Partition_Type_All(4)
# Partitions generated
PTA$Part.class
# Partitions of size 2 includes two types
PTA$eL_r[[2]]
# Number of partitions with r=1 blocks, r=2 blocks, etc-
PTA$S_N_r
# Number of different types collected by  partitions of size r=1, r=2, etc.
PTA$S_r_j
# Partitions with size r=2, includes two types (above) each with number
PTA$S_r_j[[2]]